Direct Methods for Transient Stability Analysis of Power Systems: Recent Results

Proceedings of the IEEE

Volumn 73, Issue 12, 1985, Pages 1703-1715

  Varaiya, Pravin ^a   Wu, Felix F ^a   Chen, Rong Liang ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLUX DECAY; TRANSFER CONDUCTANCES; TRANSIENT STABILITY ANALYSIS; VOLTAGE-DEPENDENT REACTIVE POWER DEMAND;

DYNAMICS - MATHEMATICAL MODELS; ELECTRIC NETWORKS - REACTIVE POWER; SYSTEM STABILITY - LYAPUNOV METHODS; SYSTEMS ANALYSIS - THEORY;

ELECTRIC POWER SYSTEMS;

EID: 0022188508     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/PROC.1985.13366     Document Type: Article

References (71)

1. E. H. Abed and P. P. Varaiya “Nonlinear oscillations in power systems,” Electric Power Energy Syst., vol. 6, no. 1., pp. 37–43, Jan. 1984.
2. P. M. Anderson and A. A. Fouad, Power System Control and Stability, vol. 1. Ames, IO: Iowa State Univ. Press, 1977.
3. A. Arapostathis, S. Sastry, and P. Varaiya “Analysis of power-flow flow equation,” Electrical Energy Power Syst., vol. 3, no. 3, pp. 115–126, July 1981.
4. T. Athay, V. R. Sherket, R. Podmore, S. Virmani, and C. Puech, “Transient energy stability analysis,” in Proc. Conf. on System Engineering for Power: Emergency Operating State Control—Section IV (Davos, Switzerland, 1979).
5. T. Athay, R. Posmore, and S. Virmani, “A practical method for direct analysis of transient stability,” IEEE Trans. Power App. Syst., vol. PAS-98, no. 2, pp. 573–584, Mar./Apr. 1979.
6. P. D. Aylett “The energy-integral criterion of transient stability limits of power systems,” Proc. Inst. Elec. Eng. (London), vol. 105 pt. C, pp. 527–536, July 1958.
7. J. Bailleul and C. I. Byrnes “Geometric critical point analysis of lossless power system models,” IEEE Trans. Circuits Syst., vol. CAS-29, no. 11, pp. 724–737, Nov. 1982.
8. A. R. Bergen, “Analytical methods for the problem of dynamic security,” in Proc. 1977 IEEE Int. Symp. on Circuits and Systems (Phoenix, AZ, Apr. 1977), pp. 864–872.
9. A. R. Bergen and D. J. Hill “A structure preserving model for power system stability analysis,” IEEE Trans. Power App. Syst., vol. PAS-100 no. 1, pp. 25–35, Jan. 1981.
10. A. R. Bergen, D. J. Hill, and C. L. De Marco, “A Lyapunov function for multimachine power systems with generator flux decay and voltage dependent loads,” Tech. Rep. EE8408, Dep. Elec. and Comput. Eng., Univ. of Newcastle, N.S.W., Australia.
11. K. S. Chandrasekhar and D. J. Hill, “Dynamic security dispatch: Basic formulation,” paper 83 WM 031-2, presented at the IEEE-PES Winter Power Meet., New York, Feb. 1983.
12. C. L. De Marco and A. R. Bergen, “Application of singular perturbation techniques to power system transient stability analysis,” Memo M84/7, Electron. Res. Lab., Univ. of California, Berkeley, CA, Feb. 20, 1984.
13. F. P. de Mello, and C. Concordia, “Concepts of synchronous machine stability as affected by excitation control,” IEEE Trans. Power App. Syst., vol PAS-88, no. 4, pp. 316–329, Apr. 1989.
14. A. H. El-Abiad and K. Nagappan, “Transient stability regions for multimachine power systems,” IEEE Trans. Power App. Syst., vol PAS-85, no. 2, pp. 169–179, Feb. 1966.
15. ESCA Corp., “Contribution to power system state estimation and transient stability analysis,” Final Rep. to DOE, Feb. 1984.
16. A. A Fouad, “Stability theory-criteria for transient stability,” in Proc. Engineering Foundation Conf. on System Engineering for Power (Henniker, NH, 1975), pp. 421–450.
17. A. A. Fouad, K. C. Kruempel, K. R. C. Mamandur, M. A. Pai, S. E. Stanton, and V. Vittal, “Transient stability margin as a tool for dynamic security assessment,” EPRI Rep. E1-1755, Mar. 1981.
18. C. E. Gless “Direct method of Lyapunov applied to transient power system stability,” IEEE Trans. Power App. Syst., vol. 85, no. 2, pp. 159–168, Feb. 1966.
19. W. Hahn, Theory and Application of Liapunov's Direct Method. Englewood Cliffs, NJ: Prentice-Hall, 1963.
20. L. B. Jocic, “Transient stability of dissipative systems,” in Proc. 9th World Congr. of IFAC, vol. 1 (Budapest, Hungary, July 2–6, 1984), pp. 26–31.
21. IEEE Committee Report, Symposium on Reliability Criteria for System Dynamic Performance, IEEE Publ. 77 CH1221-1-PWR, pp. 8–11, 1977.
22. N. Kakimoto, Y. Ohnogi, M. Matsuda, and H. Shibuya “Transient stability analysis of large-scale power systems by Lyapunov's direct method,” IEEE Trans. Power App. Syst., vol. PAS-103 no. 1, pp. 160–167, Jan. 1984.
23. N. Kakimoto, Y. Ohsawa, and M. Hayashi, “Transient stability analysis of electric power systems via Lure type Lyapunov function, Part I. New critical value for transient stability; Part II. Modification of Lure type Lyapunov function with effect of transfer conductances,” Trans. IEE of Japan, vol. 98, no. 5/6, pp. 62–71; 72–79, May/June 1978.
24. —, “Transient stability analysis of multimachine power systems with flux decay via Lyapunov's direct method,” IEEE Trans. Power App. Syst., vol. PAS-99, no. 5, pp. 1819–1827, Sept./Oct. 1980.
25. R. J. Kaye and F. F. Wu “Dynamic security regions for power systems,” IEEE Trans. Circuits Syst., vol. CAS-29, no. 9, pp. 612–623, Sept. 1982.
26. N. Kopell and R. B. Washburn, Jr. “Chaotic motion in two-degree-of-freedom swing equations,” IEEE Trans. Circuits Syst., vol. CAS-29, no. 11, pp. 738–746, Nov. 1982.
27. A. I. Mees and L. O. Chua “The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems,” IEEE Trans. Circuits Syst., vol. CAS-26, no. 4, pp. 235–254, Apr. 1979.
28. A. N. Michel, A. A. Fouad, and V. Vittal “Power system transient stability using individual machine energy functions,” IEEE Trans. Circuits Syst., vol. CAS-30, no. 5, pp. 266–276, May 1983.
29. A. N. Michel and R. K. Miller, Qualitative Analysis of Large Scale Dynamical Systems. New York, NY: Academic Press, 1977.
30. N. Narasimhamurthi “On the existence of energy function for power systems with transmission losses,” IEEE Trans. Circuits Syst., vol. CAS-31, pp. 199–203, Feb. 1984.
31. N. Narasimhamurthi and M. R. Musavi “A general energy function for transient stability analysis of power systems,” IEEE Trans. Circuits Syst., vol. CAS-31, no. 7, pp. 637–645, July 1984.
32. V. V. Nemyetskii and V. V. Stepanov, Qualitative Theory of Differential Equations. Princeton, NJ: Princeton Univ. Press, 1960.
33. M. A. Pai, “Some mathematical aspects of power system stability by Lyapunov's method,” presented SIAM Int. Conf. on Electric Power Problems: The Mathematical Challenge, Seattle WA, Mar. 18–20, 1980.
34. M. A. Pai, Power System Stability—Analysis by the Direct Method of Lyapunov. New York, NY: North Holland, 1981.
35. Panel Report, “Application of direct methods to transient stability analysis of power systems,” paper 84 WM 070-9, presented at the IEEE Power Engineering Society Winter Meeting, Dallas, TX, Jan. 29–Feb. 3, 1984.
36. F. S. Prabhakara and A. H. El-Abiad, “A simplified determination of transient stability in power systems,” IEEE Trans. Power App. Syst., vol. PAS-94, no. 2, pp. 672–680, Mar./Apr. 1975.
37. M. Ribbens-Pavella, “Critical survey of transient stability studies of multimachine power systems by Lyapunov's direct method,” in Proc. 9th Annual Allerton Conf. on Circuits and System Theory, Oct. 1971.
38. M. Ribbens-Pavella, L. T. Grujic, J. Sabatel, and A. Bouffioux, “Direct methods for stability analysis of large scale power systems,” in Proc. IFAC Symp. on Computer Applications in Large Scale Power Systems (New Delhi, India, Aug. 16–18, 1979). New York: Pergamon Press, 1979.
39. M. Ribbens-Pavella, A. Calvaer, and J. Gheury, “Transient stability index for on-line evaluation,” in Preprints, IEEE PES Winter Meeting (New York, NY, Feb. 3–8, 1980).
40. M. Ribbens-Pavella, P. G. Murthy, and J. L. Horward, “The acceleration approach to practical transient stability domain estimation in power systems,” in Proc. 20th IEEE Conf. on Decision and Control, (San Diego, CA, Dec. 16–18, 1981), pp. 471–477.
41. M. Ribbens-Pavella, J. L. Horward, and S. Chebbi, “On the effectiveness of direct methods in the study of power system transient stability,” presented at the CIGRE/IFAC symp. on Control Applications for Power System Security, Florence, Italy, Sept. 26–28, 1983.
42. F. M. A. Salam, A. Arapostathis, and P. Varaiya, “Analytic expressions for the unstable manifold at equilibrium points in dynamical systems of differential equations,” in Proc. 22nd Conf. on Decision and Control (San Antonio, TX, Dec. 14–16, 1983), pp. 1389–1392.
43. F. M. A. Salam, J. E. Marsden, and P. P. Varaiya “Arnold diffusion in the swing equations of a power system,” IEEE Trans. Circuits Syst., vol. CAS-31, no. 8, pp. 673–688, Aug. 1984.
44. — “Chaos and Arnold diffusion in dynamical systems,” IEEE Trans. Circuits Syst., vol. CAS-30, no. 9, pp. 697–708, Sept. 1983.
45. H. S. Y. Sastry, “Application of topology energy functions for the direct stability evaluation of power systems,” Ph.D. dissertation, Dep. Elec. Eng., Indian Institute of Technology, Kanpur, India, May 1984.
46. S. S. Sastry and P. Varaiya “Hierarchical stability and alert state steering control of interconnected power systems,” IEEE Trans. Circuits Syst., vol. CAS-27, no. 11, pp. 1102–1112, Nov. 1980.
47. S. Shahshahani “Dissipative systems on manifolds,” Inventiones Mathematicae, vol. 16, pp. 177–190, 1972.
48. D. D. Siljak, Large Scale Dynamic Systems—Stability and Structure. New York, NY: North Holland, 1978.
49. D. D. Siljak, Large Scale Dynamic Systems—Stability and Structure. New York, NY: North Holland, 1978.
50. B. Stott “Power system dynamic response calculations,” Proc. IEEE., vol. 67, no. 2, pp. 219–241, Feb. 1979.
51. S. N. Talukdar and F. F. Wu “Computer-aided dispatch for electric power system,” Proc. IEEE, vol. 69, no. 10, pp. 1212–1231, Oct. 1981.
52. N. Tsolas, “Stability and computer simulation of power systems,” Ph. D. dissertation, Dep. Elec. Eng. and Comput. Sci., Univ. of California, Berkeley, CA, Oct. 1983.
53. N. Tsolas, A. Arapostathis, and P. Varaiya “A structure preserving energy function for power system transient stability analysis,” IEEE Trans. Circuits Syst., vol. CAS-32, no. 10, pp. 1041–1049, Oct. 1985.
54. J. E. Van Ness, F. M. Brasch, Jr., G. L. Landgren, and S. I. Neumann, “Analytical investigations of dynamic instability occurring at powerton station,” IEEE Trans. Power App. Syst., vol. PAS-99, no. 4, pp. 1386–1395, July/Aug. 1980.
55. M. Vidyasagar, Nonlinear Systems Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1978.
56. V. Vittal, “Power system transient stability using critical energy of individual machines,” Ph.D. dissertation, Iowa State Univ., Ames, IO, 1982.
57. J. L. Willems “Optimum Lyapunov functions and stability regions for multimachine power systems,” Proc. Inst. Elec. Eng., vol. 117, no. 3, pp. 573–577, Mar. 1970.
58. — “Direct methods for transient stability studies in power systems analysis,” IEEE Trans. Automat. Contr., vol. AC-16, no. 4, pp. 332–341, Aug. 1971.
59. F. F. Wu, “Stability, security, and reliability of interconnected power systems,” Large Scale Systems: Theory and Applications, to appear.
60. F. F. Wu, “Probabilistic steady-state and dynamic security assessment,” Final Rep. to Dep. of Energy. Mar. 2, 1984.
61. F. F. Wu and Y-K. Tsai “Probabilistic dynamic security assessment of power systems, Part I: Basic mode,” IEEE Trans. Circuits Syst., vol. CAS-30, no. 3, pp. 148–159, Mar. 1983.
62. —, “Probabilistic steady-state and dynamic security assessment,” IEEE Trans. Power App. Syst., to be published.
63. H. Yee and B. D. Spaulding “Transient stability analysis of multimachine power systems by the method of hyperplanes,” IEEE Trans. Power App. Syst., vol. PAS-96, no. 1, pp. 276–284, Jan. 1977.
64. O. Sato, K. Koziumi, M. Udo, M. Saito, H. Mukae and T. Tsuji, “Security monitoring systems including fast transient stability studies,” IEEE Trans. Power App. Syst., vol. PAS-94, no. 5, pp. 1789–1805, Sept./Oct. 1975.
65. H. Hakimmashhadi and G. T. Heydt, “Fast transient security assessment,” paper 83 SM 350-6, presented at the IEEE PES Summer Meeting, Los Angeles, CA, July 1983.
66. C. L. Gupta and A. H. El-Abiad, “Determination of the closest unstable equilibrium state for Liapunov methods in transient stability studies,” IEEE Trans. Power App. Syst., vol. PAS-95, no. 5, pp. 1699–1712, Sept./Oct. 1976.
67. A. Shalaby “On-line computer monitoring of complex power system stability limits,” in Proc. 1979 PICA Conf. (Cleveland, OH), pp. 64–72.
68. V. Vittal, A. N. Michel, and A. A. Fouad “Power system transient stability analysis: formulation as nearly Hamiltonian systems,” Circuits, Syst. Signal Processing, vol. 3, no. 1, pp. 106–122, 1984.
69. D-H Chiang and F. F. Wu, “An explicit characterization of stability boundary and its application to power system transient stability analysis,” IEEE Trans. Circuits Syst., to be published.
70. C. L. Gupta and A. H. El-Abiad, “Transient security assessment of power systems by pattern recognition—A pragmatic approach,” in Proc. IFAC symp., pp. 359–363, Feb. 1977.
71. —, “Transient security assessment of power systems by pattern recognition—A statistical approach,” paper A77 592-9 presented at the IEEE Summer PES Meet., Mexico City, July 1977.